Independent ratio of linear combinations of chi square variables

Linear combinations of chi square variables have already been implemented in Matlab, so I thought it should be also the case for the independent ratio.

More precisely, I want to compute the quantiles of the ratio of $X$, which is a chi square variable with $r_1$ degrees of freedom and independent from $Y$, and $Y$, which is a linear combination of independent central chi square variables.

Kind regards, Mohamed

[Tom Lane]

When you write that linear combinations of chi-square variables are implemented, what do you have in mind?

The ratio of two independent chi-squares has an F distribution (or a multiple of one). I don't know the distribution if the denominator is a linear combination of chi-squares.